Advertisements
Advertisements
Question
Examine the consistency of the following equation:
x + 2y −3 = 0, 7x + 4y − 11 = 0, 2x + 4y − 6 = 0
Solution
The given equations are
x + 2y −3 = 0,
7x + 4y − 11 = 0,
2x + 4y − 6 = 0
These equations are consistent, if
`|(1, 2, -3),(7, 4, -11),(2, 4, -6)| = 0, "provided" |(1, 2),(7, 4)| ` ≠ 0 which is obviously true.
Now, L.H.S. = `|(1, 2, -3),(7, 4, -11),(2, 4, -6)|`
= 1(–24 + 44) – 2(–42 + 22) – 3(28 – 8)
= 1(20) – 2(–20) – 3(20)
= 20 + 40 – 60
= 0
= R.H.S.
∴ The given equations are consistent.
APPEARS IN
RELATED QUESTIONS
Examine the consistency of the following equation:
2x − y + 3 = 0, 3x + y − 2 = 0, 11x + 2y − 3 = 0
Examine the consistency of the following equation:
2x + 3y − 4 = 0, x + 2y = 3, 3x + 4y + 5 = 0
Find k if the following equations are consistent:
2x + 3y - 2 = 0, 2x + 4y − k = 0, x − 2y + 3k =0
Find k if the following equations are consistent:
kx + 3y + 1 = 0, x + 2y + 1 = 0, x + y = 0
Answer the following question:
Find the value of k, if the following equations are consistent:
(k + 1)x + (k – 1)y + (k – 1) = 0
(k – 1)x + (k + 1)y + (k – 1) = 0
(k – 1)x + (k – 1)y + (k + 1) = 0
Answer the following question:
Find the value of k, if the following equations are consistent:
3x + y − 2 = 0 kx + 2y − 3 = 0 and 2x − y = 3
Answer the following question:
Find the value of k if the following equation are consistent:
(k − 2)x + (k − 1)y = 17 , (k − 1)x + (k − 2)y = 18 and x + y = 5
Answer the following question:
Find the area of triangle whose vertices are L(1, 1), M(−2, 2), N(5, 4)
Answer the following question:
Show that the lines x − y = 6, 4x − 3y = 20 and 6x + 5y + 8 = 0 are concurrent. Also find the point of concurrence
